OFFSET
1,12
COMMENTS
a(n) divides A003557 but is not equal to it.
a(n) is least d such that the prime power exponents of n/d are all equal; see also A066636. - David James Sycamore, Jun 13 2024
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n/A062759(n). - Amiram Eldar, Feb 12 2023
EXAMPLE
n=1800: the squarefree kernel is 2*3*5 = 30 and 900 = 30^2 divides n, a(1800) = 2, the quotient of 1800/900.
MAPLE
f:= proc(n) local F, m, t;
F:= ifactors(n)[2];
m:= min(seq(t[2], t=F));
mul(t[1]^(t[2]-m), t=F)
end proc:
map(f, [$1..200]); # Robert Israel, Nov 03 2017
MATHEMATICA
{1}~Join~Table[n/#^IntegerExponent[n, #] &@ Last@ Select[Divisors@ n, SquareFreeQ], {n, 2, 104}] (* Michael De Vlieger, Nov 02 2017 *)
a[n_] := Module[{f = FactorInteger[n], e}, e = Min[f[[;; , 2]]]; f[[;; , 2]] -= e; Times @@ Power @@@ f]; Array[a, 100] (* Amiram Eldar, Feb 12 2023 *)
PROG
(PARI)
A007947(n) = factorback(factorint(n)[, 1]); \\ Andrew Lelechenko, May 09 2014
A051904(n) = if(1==n, 0, vecmin(factor(n)[, 2])); \\ After Charles R Greathouse IV's code
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 16 2001
STATUS
approved